Large deviations of local times of Levy processes

For X(t) a real-valued symmetric Levy process. its characteristic function is E(e(i lambda X(t))) = exp( - t psi(lambda)). Assume that psi is regularl y varying at infinity with index 1 < beta less than or equal to 2. Let L-t( x) denote the local time of X(t) and L-t* = sup(x is an element of R) L-t(x ). Estimates are obtained for P(L-t(0) greater than or equal to y) and P(L- t* greater than or equal to y) as y --> infinity and t fixed.